The invention relates to an apparatus for determining a measured value during the arrival of an ATM cell which forms part of an ATM cell flow in an ATM system. Such an apparatus is disclosed, inter alia, in European Patent Application EP-381 275 in the name of the Applicant. This is used to protect an ATM system against impermissible transgressions of the nominal (maximum) cell rates assigned to the cell flows (virtual channels) provided. The known apparatus makes use of a so-called `leaky bucket` mechanism. A problem which occurs in the transmission of ATM cells is that, as a consequence of the individual manipulability thereof, the cells may have a fairly large variation in arrival time (cell delay variation). Insofar as this variation is a consequence of manipulations in the transmission system itself (such as in switches and buffers) (see, inter alia, European Patent Application EP-450 708 in the name of the Applicant), this must not result in the cells being rejected. On the other hand, cell series which do (substantially) exceed the cell rate through the fault of the users are in fact refused further transmission (or, for example, marked as in European Patent 0 275 678 in the name of AT&T). The said `leaky bucket` mechanism has too few degrees of freedom to monitor the cell flow accurately enough for it to be possible to deduce with a reasonable probability from the measured value obtained whether a (temporary) cell rate increase is the consequence of an unavoidable variation induced by the transmission system or the consequence of an unduly high cell rate (which is in fact avoidable) on the part of the system users.